MasterTool

True Airspeed Calculator

Calculate true airspeed with the standard wind-triangle / ISA formulas.

Loading calculator…

What this tool does

Calculate true airspeed with the standard wind-triangle / ISA formulas. Uses calibrated airspeed as the starting point (position/instrument error already corrected) and the ISA pressure relation with your actual OAT. At 10,000 ft the ISA temperature is about −5 °C; a warmer OAT lowers density and raises TAS further.

How to use the True Airspeed Calculator

  1. Enter or select indicated / calibrated airspeed (knots).
  2. Enter or select pressure altitude (ft).
  3. Enter or select outside air temperature (°c).
  4. Read the calculated result; change any measurement to compare alternatives.

Formula

ISA pressure ratio δ = (1 − 6.87535×10⁻⁶ × pressure altitude ft)^5.2561; temperature ratio θ = OAT (K) ÷ 288.15; density ratio σ = δ ÷ θ; TAS = CAS ÷ √σ
cas
Indicated / calibrated airspeed (knots)
altitude
Pressure altitude (ft)
oat
Outside air temperature (°C)

Uses calibrated airspeed as the starting point (position/instrument error already corrected) and the ISA pressure relation with your actual OAT. At 10,000 ft the ISA temperature is about −5 °C; a warmer OAT lowers density and raises TAS further.

Worked example

For true airspeed calculator, the following measurements illustrate the exact method: Indicated / calibrated airspeed (knots): 100; Pressure altitude (ft): 10000; Outside air temperature (°C): -5.

Inputs

  • Indicated / calibrated airspeed (knots)100
  • Pressure altitude (ft)10000
  • Outside air temperature (°C)-5

Result

  • True airspeed (knots)116.33
  • Density ratio (σ)0.74
  • Pressure ratio (δ)0.69
  • ISA temperature at this altitude (°C)-4.81
  • Speed of sound at OAT (knots)638.32
  • Approximate Mach number0.18

Results explained

True airspeed (knots)
True airspeed (knots) from the formula above. Uses calibrated airspeed as the starting point (position/instrument error already corrected) and the ISA pressure relation with your actual OAT. At 10,000 ft the ISA temperature is about −5 °C; a warmer OAT lowers density and raises TAS further.
Density ratio (σ)
Density ratio (σ) from the formula above. Uses calibrated airspeed as the starting point (position/instrument error already corrected) and the ISA pressure relation with your actual OAT. At 10,000 ft the ISA temperature is about −5 °C; a warmer OAT lowers density and raises TAS further.
Pressure ratio (δ)
Pressure ratio (δ) from the formula above. Uses calibrated airspeed as the starting point (position/instrument error already corrected) and the ISA pressure relation with your actual OAT. At 10,000 ft the ISA temperature is about −5 °C; a warmer OAT lowers density and raises TAS further.
ISA temperature at this altitude (°C)
ISA temperature at this altitude (°C) from the formula above. Uses calibrated airspeed as the starting point (position/instrument error already corrected) and the ISA pressure relation with your actual OAT. At 10,000 ft the ISA temperature is about −5 °C; a warmer OAT lowers density and raises TAS further.
Speed of sound at OAT (knots)
Speed of sound at OAT (knots) from the formula above. Uses calibrated airspeed as the starting point (position/instrument error already corrected) and the ISA pressure relation with your actual OAT. At 10,000 ft the ISA temperature is about −5 °C; a warmer OAT lowers density and raises TAS further.
Approximate Mach number
Approximate Mach number from the formula above. Uses calibrated airspeed as the starting point (position/instrument error already corrected) and the ISA pressure relation with your actual OAT. At 10,000 ft the ISA temperature is about −5 °C; a warmer OAT lowers density and raises TAS further.

Frequently asked questions

First correct IAS for instrument and position error to get CAS, then divide by the square root of the density ratio: TAS = CAS ÷ √σ. This tool does the second step with σ from the ISA pressure formula and your OAT — 100 kt CAS at 10,000 ft on an ISA day gives about 116 kt TAS.

An airspeed indicator measures dynamic pressure, and thin air at altitude produces less pressure at the same true speed. The indicator therefore under-reads as density falls — roughly 2% per 1,000 ft — so TAS grows above CAS the higher you climb.

Your actual outside air temperature at altitude. The default −5 °C is the ISA temperature at 10,000 ft (15 °C at sea level minus about 1.98 °C per 1,000 ft). Warmer-than-ISA air is less dense, so TAS will be higher than the ISA value.

IAS is what the gauge shows. CAS is IAS corrected for instrument and position error (from the POH table). TAS is CAS corrected for air density — the speed the aircraft actually moves through the air mass, and the starting point for groundspeed once wind is applied.

TAS is the input the wind triangle needs — combine it with wind in the Wind Correction Calculator to get groundspeed. Like all results here it is a planning estimate: verify against the POH cruise tables and official weather before flight.